Course Syllabus

  • First order equations.
    • First order linear and nonlinear equations: analytic methods for solving linear equations, separable equations and exact equations.
    • Modeling with linear first order equations: exponential growth and decay; mixing problems; interest rates; and others.
    • Modeling with nonlinear first order equations, geometric methods and qualitative analysis, population models, phase portrait and classification of equilibrium points.
  • Second order equations.
    • Theory, linearity principle.
    • Homogenous second order linear differential equations with constant coefficients. Real, complex roots, and repeated roots.
    • Inhomogeneous second order linear differential equations: methods of undetermined coefficients.
    • Modeling with linear second order equations: Mechanical and electrical oscillations. Forcing and resonances.
  • Laplace transform methods.
    • Laplace transform for initial value problems.
    • Discontinuous forcing.
    • Impulse functions and convolutions.
  • Systems of linear differential equations: eigenvalues and eigenvectors, phase portraits.
    • Review of linear algebra: matrices, eigenvalues and eigenvectors.
    • System of linear equations with constant coefficients: solving initial value problems with real and complex eigenvalues.
    • Classification of equilibrium points, sinks, sources, saddles, centers, spiral sinks and spiral sources.

Prerequisites: Math 131 & 132.

Text: Elementary Differential Equations, 11th edition, by Boyce, DiPrima and Meade.